The exception that proves the rule

There are two common interpretations of this phrase, neither of which captures the original meaning. The most common interpretation is that no rule is absolute: an exception to a rule confirms that the rule is actually a reasonable rule and not, say, a tautology.

Of course, this is silly, leading others to claim a different meaning. According to this second interpretation, 'prove' in this phrase means 'to test', as it does in the aphorism "The proof is in the pudding". That is, "X is the exception that proves the rule Y" means that X is an exception to Y, and that the existence of an exception strains the truth of the assertion Y, or even disproves it.